Sensitivity analysis and publication bias
A leave-one-out sensitivity analysis was conducted among studies examining the association between lubricants and perineal trauma, episiotomy, first- and second-degree perineal laceration. The sensitivity analysis shows that none of these studies was found to have substantially altered the overall results of the analysis (Appendix S2). Publication bias for four outcomes (perineal trauma, episiotomy, first- and second-degree perineal laceration) was calculated using the funnel plot (Appendix S3), and there was no evident asymmetry. Moreover, Begg’s test showed that there was no obvious publication bias (P =0.32,P =0.09, P =1 and P =0.37 for perineal trauma, episiotomy, first- and second-degree perineal laceration, respectively).